advection equation

[amazing]

Hi every body
i wanna to find the solution of the advection equation u(x,t)with the following intial and boundary condtion.


\(\displaystyle \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial t}=0\)
\(\displaystyle u(x,0)=sin(kx)\) intial condition[
\(\displaystyle u(0,t)=sin(wt)\)boundary condition

 

[Deleted member 4993]

Hi every body
i wanna to find the solution of the advection equation u(x,t)with the following intial and boundary condtion.


\(\displaystyle \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial t}=0\)
\(\displaystyle u(x,0)=sin(kx)\) intial condition[
\(\displaystyle u(0,t)=sin(wt)\)boundary condition

Please check your equation and correct it as needed.

 

[amazing]

Hi every body
i wanna to find the solution of the advection equation u(x,t)with the following intial and boundary condtion.


\(\displaystyle \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial x}=0\)
\(\displaystyle u(x,0)=sin(kx)\) intial condition[
\(\displaystyle u(0,t)=sin(wt)\)boundary condition

 

[Deleted member 4993]

Hi every body
i wanna to find the solution of the advection equation u(x,t)with the following intial and boundary condtion.


\(\displaystyle \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial x}=0\)
\(\displaystyle u(x,0)=sin(kx)\) intial condition[
\(\displaystyle u(0,t)=sin(wt)\)boundary condition

These types of equation has a general solution of the kind:

u = u[sub:284rlts6]0[/sub:284rlts6][x-c(t-t[sub:284rlts6]0[/sub:284rlts6])]

where

u(x,t[sub:284rlts6]0[/sub:284rlts6]) = u[sub:284rlts6]0[/sub:284rlts6](x)

Can you go from there?

 

[amazing]

but can this solution show the effect of the boundary condition propagation
for example if the boundary condition is zero then by the time the solution become zeros can this solution show the propagation of the boundary
can we have asolution which show us this effect.